where the Lagrange parameters \(\lbrace \beta _n(x,t)\rbrace \)  now depend on \((x,t)\) . Integrating the conservation laws (REF ) over a contour \([0,X]\times [0,T]\)  and taking the average under approximation (REF ) we may write [1]}
\(\int _{0}^{X} {\rm d}x\,\left[\bar{q}_n(x,T)-\bar{q}_n(x,0)\right] + \int _{0}^{T}{\rm d}t\,\left[\bar{j}_n(X,t)-\bar{j}_n(0,t)\right]=0 \; .\) 
